Camera Labs

I recently purchased a 5D3. Aside from using a tripod, and as I understand, on long exposures there are 3 features that reduce/eliminate camera shake: mirror lockup, timed exposure and electronic remote. I would like to combine 2 features i.e. mirror lockup and timed exposure or mirror lockup and electronic remote but I can't seem to make these work. Any advice?

Good purchase. Hopefully you have learned more about this camera in the last month.
Using a solid tripod will also help when doing long exposures. Both mirror lockup and time delays are available through the menu.
Mirror lockup will require 2 shutter presses. 1st one raises the mirror and 2nd one opens the curtains for exposure.

I use a remote switch so I don't touch the camera but the time delay works too.

Using a long lens also makes it more difficult to keep any shake out.

Here is a 25 second exposure at ISO 100 where I used a gimbal head on a carbon fiber Manfrotto tripod and Canon 300mm F/4 L lens. I used mirror lockup.
The 5D Mk III is awesome.

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DSLRs: Canon 5D Mk III, Canon 60D
Lenses: Canon 16-35 F/2.8L, Canon 70-200 F/4L, Canon 300 F/4L IS, Tamron 90 2.8 Macro, Tamron 24-70 DI VC, Sigma 35mm 1.4 DG
Flash: Canon 600 EX(2), Canon ST-E3-RT, Alien Bees B800